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Propagation of Chaos for the Thermostatted Kac Master Equation

Journal article
Authors E. Carlen
Dawan Mustafa
Bernt Wennberg
Published in Journal of statistical physics
Volume 158
Issue 6
Pages 1341-1378
ISSN 0022-4715
Publication year 2015
Published at Department of Mathematical Sciences
Department of Mathematical Sciences, Mathematics
Pages 1341-1378
Language en
Links dx.doi.org/10.1007/s10955-014-1155-...
Keywords Master equation, Propagation of chaos, Kinetic equation with a thermostat
Subject categories Mathematics

Abstract

The Kac model is a simplified model of an -particle system in which the collisions of a real particle system are modeled by random jumps of pairs of particle velocities. Kac proved propagation of chaos for this model, and hence provided a rigorous validation of the corresponding Boltzmann equation. Starting with the same model we consider an -particle system in which the particles are accelerated between the jumps by a constant uniform force field which conserves the total energy of the system. We show propagation of chaos for this model.

Page Manager: Webmaster|Last update: 9/11/2012
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